To graph 2x-3y=12, we might start with a table of values in which we set first x to 0, then y:<\/p>\n
![](\"\/blog\/blogfiles\/ineqtab0.png\")
<\/p>\n
To find y when x=0, we substitute 0 in for x and solve:<\/p>\n
2(0)-3y=12<\/p>\n
-3y=12<\/p>\n
Dividing both sides by -3 gives<\/p>\n
y=-4<\/p>\n
Next, we find x when y=0:<\/p>\n
2x-3(0)=12<\/p>\n
2x=12<\/p>\n
Dividing both sides by 2 gives<\/p>\n
x=6<\/p>\n
We can complete our table now:<\/p>\n
![](\"\/blog\/blogfiles\/ineqtab1.png\")
<\/p>\n
Next, we plot the two points from the table, (0,-4) and (6,0), on a graph and draw a line through them:<\/p>\n
![](\"\/blog\/blogfiles\/ineq00.png\")
<\/p>\n
We have graphed the equation 2x-3y=12. To graph the inequality<\/strong> 2x-3y\u226412, we will need to shade on one side of the line. To determine which side, we use a test point<\/strong>, which is a point not on our line<\/strong>. When we can, we like to use (0,0). In this case, we can use (0,0), since it’s not on the line we’ve drawn.<\/p>\n We plug our test point, which is in this case (0,0), into 2x-3y≤12:<\/p>\n 2(0)-3(0)≤12<\/p>\n which gives<\/p>\n 0≤12<\/p>\n Since the statement 0≤12 is true<\/span>, we shade the side (0,0) is on:<\/p>\n Points to note about graphing inequalities in general:<\/u><\/p>\n 1) If the test point makes your inequality false<\/em>, you shade the other side of the line<\/em>, not the side on which the test point is found.<\/p>\n 2) If your line passes through (0,0), you must choose another test point instead. Perhaps you could use (0,1) or (1,0) in such a case.<\/p>\n 3) If the inequality is a strict inequality (that is, it uses < or > rather than ≤ or ≥), you use a dotted line rather than a solid line.<\/p>\n While there are still more points to raise about this topic, the content here is a good primer. I’ll continue with linear inequalities and their graphs in future posts.<\/p>\n HTH:)<\/p>\n![](\"\/blog\/blogfiles\/ineq0.png\")
<\/p>\n